The 23-year-old received offers from both clubs, but the Blades emerged victorious.
Clarke is set to undergo a medical at Bramall Lane and finalize the loan for the rest of the season.
“There's a possibility that Harry Clarke will go out on loan, a possibility at the moment,” Town coach Kieran McKenna said.
“Me and Harry have had those conversations. He's an important player for us, a very good player.
“He had a big surgery (on both Achilles tendons) and played through some injury at the back end of last season. He had big surgery in the summer, so he missed a few months of football.
“He has had some minutes now in the Premier League and some exposure but for his age as a young defender it's important to be getting minutes regularly for his progression and for his role at the club.
“So, if everything is in a good place in the squad over the next week or two from an availability point of view, there's a chance that Harry will go out on loan to get some regular playing time to keep pushing with his development.”